An exposure apparatus which projects and transfers the pattern of a reticle (mask) onto a substrate by a projection optical system is employed to manufacture a semiconductor device using the photolithography technique. The projection optical system is regulated upon a step of measuring the optical characteristic (aberration), a step of calculating the amount of regulation of a regulating unit for correcting the optical characteristic based on the measured optical characteristic, and a step of regulating the regulating unit based on the calculated amount of regulation.
Also, the optical characteristic to be regulated depend on the amount of regulation of each unit (for example, lenses which constitute the projection optical system), and the maximum value of their absolute value is required to minimize at each point in the image plane (exposure region). Hence, Japanese Patent Laid-Open No. 2005-268451 proposes a technique of determining (optimizing) the amount of regulation of each unit using linear programming or quadratic programming.
Japanese Patent Laid-Open No. 2005-268451 discloses two methods for determining the amount of regulation of each unit, both of which pose the following problems. For example, the first method uses quadratic programming. With this method, the amount of regulation which minimizes the quadratic optical characteristic (for example, the (weighted) square sum of wavefront aberrations) can be obtained. However, this method uses the quadratic optical characteristic as an objective function, and therefore does not guarantee a precise optimum solution. Also, in the second method, an amount (for example, the square root of the (weighted) square sum of wavefront aberrations) corresponding to the RMS of the wavefront aberration is approximated by a linear expression which describes it as the weighted sum of the absolute values of wavefront aberration coefficients (Zernike coefficients), and a variable indicating the upper limit value of the linear expression is defined as an objective function. The amount of regulation which minimizes the value of the objective function is then solved by linear programming. This method can obtain a precise optimum solution, but may pose a problem resulting from an error of the above-mentioned approximation operation. Note that the RMS is an abbreviation for “Root Mean Square.”